Yes and no to Bede, and semi to the other.

Bed unlike most historians of his time took great pains to not only cite his sources and how he obtained them, this includes several emissaries to Rome for transcription purposes, but also in oral traditions the places where heard. In early instances he outright copies the earlier Anglo-Saxon chronicles, but still cites his sources well. He on occasion mentioned contradictory beliefs but for the most part keeps silent unless he can thoroughly prove sources.

On a grander scheme, it's impossible to know about ancient accounts on the whole, as I was told, "If we become too cynical we have nothing to work with" because sources from this time are so rare to begin with we have to look with forgiving be eyes. On that note though Bede is considered THE best source for his time.